Lens-free image sensor using phase-shifting hologram

ABSTRACT

An image sensor is provided. The image sensor includes: a plurality of photoelectric elements for receiving an incident light. The photoelectric elements are arranged into a plurality of unit cells, and each of the unit cells includes a first photoelectric element and a second photoelectric element. The first photoelectric element in each of the unit cells captures a first pixel in a first phase, and the second photoelectric element in each of the unit cells captures a second pixel in a second phase, wherein the first phase is different from the second phase.

BACKGROUND OF THE INVENTION Field of the Invention

The present invention relates to an imaging sensor and, in particular,to a lens-free image sensor using phase-shifting hologram.

Description of the Related Art

With advances being made in technology, electronic devices equipped witha camera have become very popular. However, a modular lens in aconventional camera, a.k.a. a color image sensing (CIS) device, isgenerally an essential component for capturing incoming light andconverting captured light into digital images. However, due to thelimitations of conventional imaging techniques, an image is formed witha lens, and a modular lens takes up a large portion of the availablespace within the camera. Since the size of portable electronic deviceshas become smaller and smaller, a large-sized modular lens is notappropriate for these devices.

Accordingly, there is demand for a lens-free image sensor to reduce thesize of the camera.

BRIEF SUMMARY OF THE INVENTION

A detailed description is given in the following embodiments withreference to the accompanying drawings.

An image sensor is provided. The image sensor includes: a plurality ofphotoelectric elements for receiving an incident light. Thephotoelectric elements are arranged into a plurality of unit cells, andeach of the unit cells includes a first photoelectric element and asecond photoelectric element. The first photoelectric element in each ofthe unit cells captures a first pixel in a first phase, and the secondphotoelectric element in each of the unit cells captures a second pixelin a second phase, wherein the first phase is different from the secondphase.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention can be more fully understood by reading thesubsequent detailed description and examples with references made to theaccompanying drawings, wherein:

FIG. 1 is a schematic diagram of a phase-shifting digital holographydevice;

FIG. 2A is a side view of an image sensor in accordance with anembodiment of the invention;

FIG. 2B is a top view of an image sensor in accordance with theembodiment of FIG. 2A;

FIG. 2C is an oblique view of the image sensor in accordance with theembodiment of FIG. 2A;

FIG. 2D is an oblique view of the image sensor in accordance withanother embodiment of the invention;

FIG. 3 is a flow chart of a 4-step phase-shifting holography method foruse in an image sensor in accordance with an embodiment of theinvention;

FIG. 4A is a top view of an image sensor in accordance with yet anotherembodiment of the invention;

FIG. 4B is an oblique view of an image sensor in accordance with theembodiment of FIG. 4A;

FIG. 5A is a side view of a color image sensor in accordance with anembodiment of the invention;

FIG. 5B is a top view of the color image sensor in accordance with theembodiment of FIG. 5A;

FIG. 5C is an oblique view of the color image sensor in accordance withthe embodiment of FIG. 5A;

FIG. 5D is a portion of a detailed side view in accordance with theembodiment of FIG. 5A;

FIG. 5E is another portion of a detailed side view in accordance withthe embodiment of FIG. 5A;

FIG. 6 is a flow chart of a 4-step phase-shifting holography method foruse in a color image sensor in accordance with an embodiment of theinvention;

FIG. 7A is a side view of an image sensor in accordance with anembodiment of the invention;

FIG. 7B is a top view of an image sensor in accordance with theembodiment of FIG. 7A;

FIG. 7C is an oblique view of the image sensor in accordance with theembodiment of FIG. 7A;

FIG. 7D is an oblique view of the image sensor in accordance withanother embodiment of the invention;

FIG. 8A is a side view of a color image sensor in accordance withanother embodiment of the invention; and

FIG. 8B is a top view of the color image sensor in accordance with theembodiment of FIG. 8A.

DETAILED DESCRIPTION OF THE INVENTION

The following description is of the best-contemplated mode of carryingout the invention. This description is made for the purpose ofillustrating the general principles of the invention and should not betaken in a limiting sense. The scope of the invention is best determinedby reference to the appended claims.

FIG. 1 is a schematic diagram of a phase-shifting digital holographydevice. As illustrated in FIG. 1, the phase-shifting digital holographydevice 100 includes a laser light source 110, a beam emitter 111, beamsplitters 101 and 103, a piezoelectric transducer (PZT) mirror 102, amirror 104, and a sensor array 120. The laser light that emitted fromthe laser light source 110 is further enhanced at the beam emitter 111,and the light emitted from the beam emitter is split into an objectlight and a reference light by the beam splitter 101. The referencelight is reflected by the PZT mirror 102 that phase modulates the beam.By shifting a constant phase to the reference beam, different hologramsare obtained to derive the complex amplitude of the object wave.

For example, the initial phase of the reference wave is zero and changesby π/2 at each step. Assuming a 4-step phase-shifting digital holographyalgorithm is used and the intensity of the interference patterns atdifferent phases such as 0, π/2, π, and 3π/2 can be respectivelyexpressed in the formulas (1)˜(4):I ₀=|ψ₀|²+|ψ_(r)|²+ψ₀ψ_(r)*+ψ₀*ψ_(r)  (1)I _(π/2)=|ψ₀|²+|ψ_(r)|² +jψ ₀ψ_(r) *−jψ ₀*ψ_(r)  (2)I _(π)=|ψ₀|²+|ψ_(r)|²−ψ₀ψ_(r)*−ψ₀*ψ_(r)  (3)I _(3π/2)=|ψ₀|²+|ψ_(r)|² −jψ ₀ψ_(r) *+jψ ₀*ψ_(r)  (4)

After obtaining the intensity of the interference patterns at phases 0,π/2, π, and 3π/2, the complex amplitude of the object light is given by:

$\begin{matrix}{\psi_{0} = \frac{\left( {I_{0} - I_{\pi}} \right) - {j\left( {I_{\pi/2} - I_{3\;{\pi/2}}} \right)}}{4\;\psi_{r}^{*}}} & (5)\end{matrix}$

The complex amplitude of the object light is sometimes referred to asthe complex hologram because we can retrieve the amplitude distributionof the object light in the object plane from Ψ₀ by performing digitalback-propagation.

Accordingly, the complex amplitude of the reference light must be knownin order to calculate object waves. Usually, the reference light is aplane wave or a spherical wave and therefore its phase is known withoutany measurement. One having ordinary skill in the art will appreciatethe techniques for reconstructing an object image using object waves atdifferent phases, and thus the details will be omitted here.

It should be noted that the phase-shifting digital holography device 100described in the example of FIG. 1 has to change phase at each step, andit takes time to change phase, calculate the intensities of interferencepatterns, and reconstruct the object image. Accordingly, it is notpractical to employ the device 100 in any portable electronic devicescurrently being sold on the market.

However, the concept of phase delay of the phase-shifting digitalholography algorithm can be used in an image sensor of the invention.FIG. 2A is a side view of an image sensor in accordance with anembodiment of the invention. For purposes of description, the imagesensor 200, for example, is a mono-color image sensor. As illustrated inFIG. 2A, the image sensor 200 includes a sensor array 220. The sensorarray 220 includes a plurality of photoelectric elements 221 forreceiving an incident light. The photoelectric elements 221 can beimplemented on a substrate 230 (as shown in FIG. 2C and FIG. 2D) viasemiconductor manufacturing processes. It should be noted that no lensis used in the image sensor 200 and, for purposes of description, thesensor array 220 in FIG. 2A does not show the relative height (i.e.thickness) of the photoelectric elements in the sensor array.

FIG. 2B is a top view of an image sensor in accordance with theembodiment of FIG. 2A. FIG. 2C is an oblique view of the image sensor inaccordance with the embodiment of FIG. 2A.

As illustrated in FIG. 2B, the sensor array 220 includes a plurality ofunit cells 250, where each unit cell has four photoelectric elementsarranged in a 2×2 array. For example, the photoelectric elements 251,252, 253 and 254 are different heights, and the height of each of thephotoelectric elements 251, 252, 253, and 254 represents a specificphase of a corresponding hologram. The heights of the photoelectricelements 251˜254 can be calculated using the following formula:

$\begin{matrix}{\delta_{m} = \frac{2\;\pi\;{nd}_{m}}{\lambda}} & (6)\end{matrix}$where λ denotes a specific wavelength; n denotes the refractive index ofthe material of the photoelectric elements; and δ_(m) denotes a givenphase value such as 0, π/2, π, and 3π/2. It should be noted that allphotoelectric elements in the sensor array 220 can be implemented by thesame material and thus have the same refractive index. Specifically, a4-step phase-shifting holography method is employed into thearchitecture of the image sensor 200. For example, the heights of thephotoelectric elements 251-254 are d₀, d₁, d₂, and d₃ that correspond tothe phases δ₀, δ₁, δ₂, and δ₃, respectively. The value of δ₀, δ₁, δ₂,and δ₃ are 0, π/2, π, and 3π/2, respectively. Since the heights d₀˜d₄match formula (6), the values of d₀, d₁, d₂, and d₃ can be calculated as0, λ/4n, λ/2n, and 3λ/4n, respectively. The differences of the heightsof the photoelectric elements 251˜254 are illustrated in FIG. 2C. Itshould be noted that the unit cell 250 is repeatedly arranged in thesensor array, and each of the photoelectric elements in each unit cell250 may capture a pixel in an individual phase of four different phases.For example, the photoelectric elements 251, 252, 253, and 254 in eachunit cell 250 may capture a first pixel in a first phase, a second pixelin a second phase, a third pixel in a third phase, and a fourth pixel ina fourth phase, respectively. Since the first pixel, the second pixel,the third pixel, and the fourth pixel are captured by photoelectricelements 251˜254 in each unit cell 250, and thus the location of thefirst pixel, the second pixel, the third pixel, and the fourth pixel aresubstantially the same. For example, the hologram image for δ₀ can beobtained from the captured pixel of the photoelectrical element 251 ineach unit cell 250. Similarly, the hologram images for δ₁, δ₂, and δ₃can be obtained from the captured pixel of the photoelectrical elements251, 252, 253 in each unit cell 250, respectively.

After obtaining hologram images in four phases, the object wave in theFourier domain can be obtained using formula (5). Subsequently, aninverse Fourier transform is performed on the object wave to reconstructthe object image in the spatial domain. Alternatively, a transferfunction H(x, y) for transforming the object wave in the Fourier domainto the object image in the spatial domain can be estimated in advance,and thus a convolution between the object wave and the transfer functioncan be performed to obtain the object image.

FIG. 2D is an oblique view of the image sensor in accordance withanother embodiment of the invention. In another embodiment, thepositions of the photoelectric elements 251˜254 in the unit cell 250 arethe same as those in FIG. 2B, but the heights of the photoelectricelements 251˜254 in the unit cell 250 are the same, as illustrated inFIG. 2D. For example, the photoelectric elements 251˜254 are made ofdifferent materials that have different refractive indexes.Specifically, the refractive index of the material of each photoelectricelement should follow the following formula:

$\begin{matrix}{\delta_{m} = \frac{2\;\pi\; n_{m}d}{\lambda}} & (7)\end{matrix}$

Referring to formula (7), the height d is a constant, and the refractiveindex n_(m) is a variable. The 4-step phase-shifting holography can alsobe used here. For example, the phases in the 4-step phase-shiftingholography method are π/4, 3π/4, 5π/8, and 7π/8. Given that the height dis equal to 0.5λ, the refractive indexes of the materials of thephotoelectric elements 251˜254 are ranged from 0.5˜1.2.

FIG. 3 is a flow chart of a 4-step phase-shifting holography method foruse in an image sensor in accordance with an embodiment of theinvention. In step S310, four phase-shifting hologram images indifferent phases are obtained. For example, the image sensor 200 shownin FIG. 2C or FIG. 2D can be used. For purposes of description, theimage sensor in FIG. 2C is used in the following embodiments.Specifically, the four phase-shifting hologram images correspond to thephases 0, π/2, π, and 3π/2.

In step S320, the object wave in the Fourier domain is calculatedaccording to the four phase-shifting hologram images in differentphases. For example, the intensities of the holograms in differentphases such as 0, π/2, π, and 3π/2, can be calculated using formulas(1)˜(4), and the object wave can be calculated using formula (5).However, to simplify the calculation of the object wave, the object waveφ₀ can be calculated approximately using the following formula:φ₀≈(I ₀ −I _(π))−j(I _(π/2) −I _(3π/2))  (8)

In step S330, the object image is reconstructed according to the objectwave. For example, the object wave φ₀ is in the Fourier domain and theobject image is in the spatial domain, and thus an inverse Fouriertransform can be applied on the object wave φ₀ to reconstruct the objectimage. Alternatively, a transfer function H(x, y) for transforming theobject wave in the Fourier domain to the object image in the spatialdomain can be estimated in advance, and thus a convolution between theobject wave and the transfer function can be performed to obtain theobject image.

FIG. 4A is a top view of an image sensor in accordance with yet anotherembodiment of the invention. FIG. 4B is an oblique view of an imagesensor in accordance with the embodiment of FIG. 4A. As described in theembodiment of FIG. 2B, each unit cell includes four photoelectricelements arranged in a 2×2 array. Referring to FIG. 4A, in yet anotherembodiment, the sensor array 220 includes a plurality of macro unitcells, and each macro unit cell includes four unit cells arranged in an2×2 unit cell array. Specifically, each macro unit cell includes 16photoelectric elements arranged in a 4×4 array.

For example, the macro unit cell 450 includes unit cells 410, 420, 430,and 440, and each unit cell includes four photoelectric elements, andeach photoelectric element in each unit cell captures a pixel in anindividual phase of four different phases. The heights of thephotoelectric elements in the unit cells 410, 420, 430, and 440 followthe 4-step phase-shifting holography method as described above such asphases 0, π/2, π, and 3π/2 being used. Additionally, two of the unitcells 410, 420, 430, and 440 in the macro cell unit 450 are rotated.Specifically, the unit cell 430 is rotated 90 degrees counterclockwiserelative to the unit cell 410, and the unit cell 440 is rotated 90degrees clockwise relative to the unit cell 420 in order to prevent theMoiré effect from occurring in each captured hologram image, and thecorresponding oblique view of the image sensor.

It should be noted that the rotation of the unit cells 430 and 440 shownin FIG. 4A is an example, and the invention is not limited thereto. Oneor more unit cells in the macro cell unit 450 can be rotated in apredetermined arrangement (e.g. by one or more predetermined angles) toprevent the Moiré effect.

FIG. 5A is a side view of a color image sensor in accordance with anembodiment of the invention. The color image sensor 500 includes afilter array 510 and a sensor array 520. The filter array 510 includes aplurality of color filters such as red filters 511, green filters 512,and blue filters 513. For example, two green filters, one red filter,and one blue filter are arranged into a 2×2 color filter array of aBayer pattern. The sensor array 520 includes a plurality ofphotoelectric elements 521 for receiving the incident light via thefilter array 510. The photoelectric elements 521 are arranged into aplurality of unit cells. For purposes of description, the sensor array520 in FIG. 5A does not show the relative heights of the photoelectricelements in the sensor array 520.

FIG. 5B is a top view of the color image sensor in accordance with theembodiment of FIG. 5A. FIG. 5C is an oblique view of the color imagesensor in accordance with the embodiment of FIG. 5A. As illustrated inFIG. 5B, the unit cells 530, 540, 550, and 560 are arranged in a 2×2array that corresponds to a 2×2 color filter array in the filter array510. Thus, the unit cells 530, 540, 550, and 560 receive green light,blue light, red light, and green light through 2×2 color filter array inthe filter array 510, respectively. Specifically, the four unit cells530, 540, 550, and 560 in the macro unit cell 570 are configured tocapture green, blue, red, and green pixels in four different phases suchas 0, π/2, π, and 3π/2. The design of heights of the photoelectricelements 531˜534, 541˜544, 551˜554, and 561˜564 in the unit cells 530,540, 550, and 560 may follow formula (6) as described above when thephotoelectric elements in the sensor array 520 are made of the samematerial, and thus the details will be omitted here. However, formula(6) is designed for a single color with a fixed wavelength.

Given that λ_(R), λ_(G), and λ_(B) represent the wavelengths of the redlight, green light, and blue light respectively, it can be concludedthat the relationship between the wavelengths is λ_(R)>λ_(G)>λ_(B),since the red light has the longest wavelength and the blue light hasthe shortest wavelength among red, green, and blue lights. Accordingly,assuming that the photoelectric elements in the sensor array 520 aremade of the same material, the photoelectric elements 551˜554 in theunit cell 550 for receiving the red light have relatively greaterheights than the photoelectric elements in other unit cells in the macrounit cell 670. That is, the heights of the photoelectric elements ineach unit cell are proportional to the wavelength of the received light.

For example, referring to FIG. 5C, the heights of the photoelectricelements 551˜554 in the unit cell 550 for receiving the red light arerelatively higher than those of the co-located photoelectric elements531-534 (i.e. the same phase) in the unit cell 530 for receiving thegreen light.

FIG. 5D is a portion of a detailed side view in accordance with theembodiment of FIG. 5A. FIG. 5E is another portion of a detailed sideview in accordance with the embodiment of FIG. 5A. The side view in FIG.5D shows the relative heights of the photoelectric elements 531˜532 inthe unit cell 530 for receiving the green light and the photoelectricelements 551˜552 in the unit cell 550 for receiving the red light. Forthe same phase, the photoelectric element 551 has a greater height thanthe photoelectric element 531, and the photoelectric element 552 has agreater height than the photoelectric element 532.

The side view in FIG. 5E shows the relative heights of the photoelectricelements 531˜532 in the unit cell 530 for receiving the green light andthe photoelectric elements 541˜542 in the unit cell 540 for receivingthe blue light. For the same phase, the photoelectric element 531 has agreater height than the photoelectric element 541, and the photoelectricelement 532 has a greater height than the photoelectric element 542.

Since the macro unit cell 570 is repeatedly arranged in the sensor array520, four phase-shifting hologram images are obtained by combiningpixels captured by each of the unit cells 530, 540, 550, and 560 of themacro unit cells in the sensor array 520, and thus total 16phase-shifting hologram images can be obtained. It should be noted thatthe green phase-shifting hologram image captured by the unit cell 530 isdifferent from that captured by the unit cell 560. For example, thetotal 16 phase-shifting hologram images can be (Rδ₀, Rδ₁, Rδ₂, Rδ₃),(G₁δ₀, G₁δ₁, G₁δ₂, G₁δ₃), (Bδ₀, Bδ₁, Bδ₂, Bδ₃), and (G₂δ₀, G₂δ₁, G₂δ₂,G₂δ₃), where the green phase-shifting hologram images (G₁δ₀, G₁δ₁, G₁δ₂,G₁δ₃) are captured by the unit cell 530, and the green phase-shiftinghologram images (G₂δ₀, G₂δ₁, G₂δ₂, G₂δ₃) are captured by the unit cell560.

FIG. 6 is a flow chart of a 4-step phase-shifting holography method foruse in a color image sensor in accordance with an embodiment of theinvention. Distinct from the flow chart in FIG. 3, the flow chart inFIG. 6 is for use in a color image sensor. In step S610, 16phase-shifting hologram images in different color channels and differentphases are obtained. For example, the image sensor 500 shown in FIG. 5can be used. The 16 phase-shifting hologram images are (Rδ₀, Rδ₁, Rδ₂,Rδ₃), (G₁δ₀, G₁δ₁, G₁δ₂, G₁δ₃), (Bδ₀, Bδ₁, Bδ₂, Bδ₃), and (G₂δ₀, G₂δ₁,G₂δ₂, G₂δ₃), as described above.

In step S620, the object wave in each color channel in the Fourierdomain is calculated according to the 16 hologram images in differentcolor channels and different phases.

In step S630, the object image for each color channel is reconstructedaccording to the object wave in each color channel. Specifically, thereare four color channels such as one red channel, one blue channel, andtwo green channels for a color image sensor, and the operations forcalculating the object wave and reconstructing the object image in asingle color channel can be referred to in the embodiment of FIG. 3, andthe details will not be repeated here.

Thus, four object images representing one red channel, one blue channel,and two green channels are obtained after step S330, and an image signalprocessor (not shown) coupled to the color image sensor 500 mayreconstruct the original color image using the four object images.

FIG. 7A is a side view of an image sensor in accordance with anembodiment of the invention. For purposes of description, the imagesensor 700, for example, is a mono-color image sensor. As illustrated inFIG. 7A, the image sensor 700 includes a sensor array 720. The sensorarray 720 includes a plurality of photoelectric elements 721 forreceiving an incident light. The photoelectric elements 721 can beimplemented on a substrate via semiconductor manufacturing processes. Itshould be noted that no lens is used in the image sensor 700 and, forpurposes of description, the sensor array 720 in FIG. 7A does not showthe relative height (i.e. thickness) of the photoelectric elements inthe sensor array.

FIG. 7B is a top view of an image sensor in accordance with theembodiment of FIG. 7A. FIG. 7C is an oblique view of the image sensor inaccordance with the embodiment of FIG. 7A.

As illustrated in FIG. 7B, the sensor array 720 includes a plurality ofunit cells 750, where each unit cell has two photoelectric elementsarranged in a 2×1 array. For example, the photoelectric elements 751 and752 are different heights, and the height of each of the photoelectricelements 751 and 752 represents a specific phase of a correspondinghologram. For example, a 2-step quadrature phase-shifting holographymethod is used for the sensor array 720, and two different phases may be0 and π/2. After obtaining the intensity of the interference patterns atphases 0 and π/2, the complex amplitude of the object light is given by:

$\begin{matrix}{\psi_{0} = \frac{\left( {I_{0} - {\psi_{0}}^{2} - {\psi_{r}}^{2}} \right) - {j\left( {I_{\pi/2} - {\psi_{0}}^{2} - {\psi_{r}}^{2}} \right)}}{2\;\psi_{r}^{*}}} & (9)\end{matrix}$

For example, the heights of the photoelectric elements 751 and 752 canbe calculated by the following formula:

$\begin{matrix}{\delta_{m} = \frac{2\;\pi\;{nd}_{m}}{\lambda}} & (10)\end{matrix}$

where λ denotes a specific wavelength; n denotes the refractive index ofthe material of the photoelectric elements; and δ_(m) denotes a givenphase value such as 0 and π/2 (or π and 3π/2). It should be noted thatall photoelectric elements in the sensor array 720 can be implemented bythe same material and thus have the same refractive index. Specifically,a 2-step phase-shifting holography method is employed into thearchitecture of the image sensor 700. For example, the heights of thephotoelectric elements 752 and 752 are d₀ and d₁ that correspond to thephases δ₀ and δ₁, respectively. The value of δ₀, and δ₁, are 0 and π/2(or π and 3π/2), respectively. Since the heights d₀˜d₁ match formula(10), the values of d₀ and d₁ can be calculated as 0 and λ/4n,respectively. The differences of the heights of the photoelectricelements 751 and 752 are illustrated in FIG. 7C. It should be noted thatthe unit cell 750 is repeatedly arranged in the sensor array 720, andeach of the photoelectric elements in each unit cell 750 may capture apixel in an individual phase of two different phases. For example, thephotoelectric elements 751 and 752 in each unit cell 750 may capture afirst pixel in a first phase and a second pixel in a second phase,respectively. Since the first pixel and the second pixel, are capturedby photoelectric elements 751 and 752 in each unit cell 750, and thusthe location of the first pixel and the second pixel are substantiallythe same. For example, the hologram image for δ₀ can be obtained fromthe captured pixel of the photoelectrical element 751 in each unit cell750. Similarly, the hologram image for δ₁ can be obtained from thecaptured pixel of the photoelectrical element 752 in each unit cell 750.

After obtaining hologram images in two phases, the object wave in theFourier domain can be obtained using formula (9). Subsequently, aninverse Fourier transform is performed on the object wave to reconstructthe object image in the spatial domain. Alternatively, a transferfunction H(x, y) for transforming the object wave in the Fourier domainto the object image in the spatial domain can be estimated in advance,and thus a convolution between the object wave and the transfer functioncan be performed to obtain the object image.

FIG. 7D is an oblique view of the image sensor in accordance withanother embodiment of the invention. In another embodiment, thepositions of the photoelectric elements 751 and 752 in the unit cell 750are the same as those in FIG. 7B, but the heights of the photoelectricelements 751 and 752 in each unit cell 750 are the same, as illustratedin FIG. 7D. For example, the photoelectric elements 751 and 752 are madeof different materials that have different refractive indexes.Specifically, the refractive index of the material of each photoelectricelement should follow the following formula:

$\begin{matrix}{\delta_{m} = \frac{2\;\pi\; n_{m}d}{\lambda}} & (11)\end{matrix}$

Referring to formula (11), the height d is a constant, and therefractive index n_(m) is a variable. The 2-step phase-shiftingholography can also be used here. For example, the phases in the 2-stepphase-shifting holography method are 0 and π/2 (or π and 3π/2). Giventhat the height d is equal to 0.52λ, the refractive indexes of thematerials of the photoelectric elements 751 and 752 can be calculatedusing formula (11).

FIG. 8A is a side view of a color image sensor in accordance withanother embodiment of the invention. The color image sensor 800 includesa filter array 810 and a sensor array 820. The filter array 810 includesa plurality of color filters such as red filters, green filters, andblue filters. For example, two green filters, one red filter, and oneblue filter are arranged into a 2×2 color filter array of a Bayerpattern. The sensor array 820 includes a plurality of unit cells 821that receives light via the filter array 810. For purposes ofdescription, the sensor array 820 in FIG. 8A does not show the relativeheights of the photoelectric elements in the sensor array 820.

FIG. 8B is a top view of the color image sensor in accordance with theembodiment of FIG. 8A. As illustrated in FIG. 7B, the unit cells 830,840, 850, and 860 receives green light, blue light, red light, and greenlight, respectively. Each of the unit cells 830, 840, 850, and 860 hastwo photoelectric elements, and has a corresponding color filter. Forexample, the unit cells 830, 840, 850, and 860 receive the green light,blue light, red light, and green light via the filter array 810.Specifically, a macro unit cell 870 in the form of the Bayer pattern canbe formed using the unit cells 830, 840, 850, and 860.

In the embodiment, a 2-step phase-shifting holography method is used.For example, two photoelectric elements in each unit cell have differentheights that are designed to receive pixels in different phases such as0 and π/2.

The design of heights of the photoelectric elements 831-832, 841-842,851-853, and 861-862 in the unit cells 830, 840, 850, and 860 may followformula (6) as described above when the photoelectric elements in thesensor array 820 are made of the same material, and thus the detailswill be omitted here. However, formula (6) is designed for a singlecolor with a fixed wavelength.

Given that λ_(R), λ_(G), and λ_(B) represent the wavelengths of the redlight, green light, and blue light respectively, it can be concludedthat the relationship between the wavelengths is λ_(R)>λ_(G)>λ_(B),since the red light has the longest wavelength and the blue light hasthe shortest wavelength among red, green, and blue lights. Accordingly,assuming that the photoelectric elements in the sensor array 820 aremade of the same material, the photoelectric elements 851˜852 in theunit cell 850 for receiving the red light have relatively greater heightthan the photoelectric elements in other unit cells in the macro unitcell 870.

Compared with the sensor array 520 in FIG. 5, the resolution along thevertical direction is double when using the sensor array 820 because thesize of a macro unit cell is 4×2 in the sensor array 820 while the sizeof a macro unit cell is 4×4 in the sensor array 820. However, thecomputation complexity for obtaining the object wave using the sensorarray 820 becomes higher. For example, the object wave in the 2-stepquadrature phase-shifting holography method can be calculated using thefollowing formula:

$\begin{matrix}{\psi_{0} = \frac{\left( {I_{0} - {\psi_{0}}^{2} - {\psi_{r}}^{2}} \right) - {j\left( {I_{\pi/2} - {\psi_{0}}^{2} - {\psi_{r}}^{2}} \right)}}{2\;\psi_{r}^{*}}} & (10)\end{matrix}$

In view of the above, a lens-free image sensor is provided. By arrangingphotoelectric elements with different heights, that are designed fordifferent phases in a 4-step phase-shifting holography algorithm, into asensor array, an object image can be reconstructed using thephase-shifting hologram images captured by the photoelectric elements,and thus no modular lens is required in the camera module using thelens-free image sensor, and thus the cost of the whole camera module canbe reduced and the thickness of the camera module can be thinner.

While the invention has been described by way of example and in terms ofthe preferred embodiments, it is to be understood that the invention isnot limited to the disclosed embodiments. On the contrary, it isintended to cover various modifications and similar arrangements (aswould be apparent to those skilled in the art). Therefore, the scope ofthe appended claims should be accorded the broadest interpretation so asto encompass all such modifications and similar arrangements.

What is claimed is:
 1. An image sensor, comprising: a plurality ofphotoelectric elements for receiving an incident light, wherein thephotoelectric elements are arranged into a plurality of unit cells, andeach of the unit cells comprises a first photoelectric element and asecond photoelectric element, wherein the first photoelectric element ineach of the unit cells captures a first pixel in a first phase, and thesecond photoelectric element in each of the unit cells captures a secondpixel in a second phase, wherein the first phase is different from thesecond phase, wherein a first phase-shifting hologram image and a secondphase-shifting hologram image are obtained by respectively combining thefirst pixels in the first phase and the second pixels in the secondphase captured by the unit cells.
 2. The image sensor as claimed inclaim 1, wherein each of the unit cells further comprises a thirdphotoelectric element capturing a third pixel in a third phase and afourth photoelectric element capturing a fourth pixel in a fourth phase,wherein the first phase, the second phase, the third phase, and thefourth phase are different.
 3. The image sensor as claimed in claim 2,wherein the first photoelectric element, the second photoelectricelement, the third photoelectric element, and the fourth photoelectricelement in each of the unit cells are made of a specific material, andare different heights.
 4. The image sensor as claimed in claim 3,wherein the first phase, the second phase, the third phase, and thefourth phase are 0, π/2, π, and 3π/2, respectively.
 5. The image sensoras claimed in claim 2, wherein the first photoelectric element, thesecond photoelectric element, the third photoelectric element, and thefourth photoelectric element in each of the unit cells are made ofdifferent materials, and are the same height.
 6. The image sensor asclaimed in claim 5, wherein the first phase, the second phase, the thirdphase, and the fourth phase are π/4, 3π/4, 5π/8, and 7π/8, respectively.7. The image sensor as claimed in claim 1, wherein an object wave iscalculated according to the first phase-shifting hologram image and thesecond phase-shifting hologram image, and an object image isreconstructed by applying an inverse-transform on the object wave. 8.The image sensor as claimed in claim 2, wherein a first phase-shiftinghologram image, a second phase-shifting hologram image, a thirdphase-shifting hologram image, and a fourth phase-shifting hologramimage are obtained by respectively combining the first pixels in thefirst phase, the second pixels in the second phase, the third pixels inthe third phase, and the fourth pixels in the fourth phase captured bythe unit cells.
 9. The image sensor as claimed in claim 8, wherein anobject wave is calculated according to the first phase-shifting hologramimage, the second phase-shifting hologram image, the thirdphase-shifting hologram image, and the fourth phase-shifting hologramimage, and an object image is reconstructed by applying aninverse-transform on the object wave.
 10. The image sensor as claimed inclaim 2, wherein the unit cells are arranged into a plurality of macrounit cells, and each of the macro unit cells comprises four unit cellsarranged in a 2×2 array, and at least one of the four unit cells in eachof the macro unit cells is rotated by a respective predetermined angle.11. The image sensor as claimed in claim 1, further comprising: a filterarray, comprising: a first green filter and a second green filter forextracting green light from an incident light; a red filter forextracting red light from the incident light; and a blue filter forextracting blue light from the incident light.
 12. The image sensor asclaimed in claim 11, wherein the unit cells are arranged into aplurality of macro unit cells, and each of the macro unit cellscomprises a first unit cell, a second unit cell, a third unit cell, anda fourth unit cell that are arranged into a 2×2 array, wherein the firstunit cell, the second unit cell, the third unit cell, and the fourthunit cell in each of the macro unit cells receive the green light, thegreen light, the red light, and the blue light via the first greenfilter, the second green filter, the red filter, and the blue filter,respectively.
 13. The image sensor as claimed in claim 12, wherein thefirst green filter, the second green filter, the red filter, and theblue filter are arranged into a Bayer pattern.
 14. The image sensor asclaimed in claim 13, wherein heights of the first photoelectric elementand the second photoelectric element in the first unit cell, the secondunit cell, the third unit cell, and the fourth unit cell in each of themacro unit cells are proportional to wavelengths of the green light, thegreen light, the red light, and the blue light, respectively.
 15. Theimage sensor as claimed in claim 12, wherein each of the unit cellsfurther comprises a third photoelectric element capturing a third pixelin a third phase and a fourth photoelectric element capturing a fourthpixel in a fourth phase, wherein the first phase, the second phase, thethird phase, and the fourth phase are different.
 16. The image sensor asclaimed in claim 15, wherein a first green phase-shifting hologramimage, a second green phase-shifting hologram image, a third greenphase-shifting hologram image, and a fourth green phase-shiftinghologram image are obtained by respectively combining the first pixelsin the first phase, the second pixels in the second phase, the thirdpixels in the third phase, and the fourth pixels in the fourth phasecaptured by the first unit cells, wherein a fifth green phase-shiftinghologram image, a sixth green phase-shifting hologram image, a seventhgreen phase-shifting hologram image, and an eighth green phase-shiftinghologram image are obtained by respectively combining the first pixelsin the first phase, the second pixels in the second phase, the thirdpixels in the third phase, and the fourth pixels in the fourth phasecaptured by the second unit cells, wherein a first red phase-shiftinghologram image, a second red phase-shifting hologram image, a third redphase-shifting hologram image, and a fourth red phase-shifting hologramimage are obtained by respectively combining the first pixels in thefirst phase, the second pixels in the second phase, the third pixels inthe third phase, and the fourth pixels in the fourth phase captured bythe third unit cells, wherein a first blue phase-shifting hologramimage, a second blue phase-shifting hologram image, a third bluephase-shifting hologram image, and a fourth blue phase-shifting hologramimage are obtained by respectively combining the first pixels in thefirst phase, the second pixels in the second phase, the third pixels inthe third phase, and the fourth pixels in the fourth phase captured bythe fourth unit cells.
 17. The image sensor as claimed in claim 16,wherein a first green object wave is calculated according to the firstgreen phase-shifting hologram image, the second green phase-shiftinghologram image, the third green phase-shifting hologram image, and thefourth green phase-shifting hologram image, and a first green objectimage is reconstructed by applying an inverse-transform on the firstgreen object wave, wherein a second green object wave is calculatedaccording to the fifth green phase-shifting hologram image, the sixthgreen phase-shifting hologram image, the seventh green phase-shiftinghologram image, and the eighth green phase-shifting hologram image, anda second green object image is reconstructed by applying theinverse-transform on the second green object wave, wherein a red objectwave is calculated according to the first red phase-shifting hologramimage, the second red phase-shifting hologram image, the third redphase-shifting hologram image, and the fourth red phase-shiftinghologram image, and a red object image is reconstructed by applying theinverse-transform on the red object wave, wherein a blue object wave iscalculated according to the first blue phase-shifting hologram image,the second blue phase-shifting hologram image, the third bluephase-shifting hologram image, and the fourth blue phase-shiftinghologram image, and a blue object image is reconstructed by applying theinverse-transform on the blue object wave.
 18. The image sensor asclaimed in claim 17, wherein a color image is obtained according to thefirst green object image, the second green object image, the red objectimage, and the blue object image.
 19. The image sensor as claimed inclaim 15, wherein heights of the first photoelectric element, the secondphotoelectric element, the third photoelectric element, and the fourthphotoelectric element in the first unit cell, the second unit cell, thethird unit cell, and the fourth unit cell in each of the macro unitcells are proportional to wavelengths of the green light, the greenlight, the red light, and the blue light, respectively.